Control of Untethered Soft

Grippers for Pick-and-Place Tasks

Federico Ongaro, ChangKyu Yoon, Frank van den Brink,

Momen Abayazid, Seung Hyun Oh, David H. Gracias, and Sarthak Misra

Abstract— In order to handle complex tasks in hard-to-reach environments, small-scale robots have to possess suitabledexterous and untethered control capabilities. The fabricationand manipulation of soft small-scale grippers complying to theserequirements is now made possible by advances in materialscience and robotics. In this paper, we use soft small-scalegrippers to demonstrate pick-and-place tasks. The preciseremote control is obtained by altering both the magnetic fieldgradient and the temperature in the workspace. This allows usto regulate the position and grasping configuration of the softthermally-responsive hydrogel-nanoparticle composite magneticgrippers. The magnetic closed-loop control achieves precise lo-calization with an average region-of-convergence of the gripperof 0.12±0.05 mm. The micro-sized payload can be placed with apositioning error of 0.57±0.33 mm. The soft grippers move withan average velocity of 0.72±0.13 mm/s without a micro-sizedpayload, and at 1.09±0.07 mm/s with a micro-sized payload.

I. INTRODUCTION

The ability of untethered small-scale robots to handle

nontrivial tasks has been demonstrated in a broad vari-

ety of applications, such as manipulation, assembly and

microactuation [1], [2]. However, traditional small robots

are often passive with no shape-changing capabilities. This

results in a limited dexterity that restricts the complexity

of achievable tasks. In contrast, robots with gripping ca-

pabilities provide significant advantages in achieving com-

plex tasks. Small-scale grippers have enabled a wide set

of applications, like precise micro-assembly, minimally in-

vasive surgery, genetics, cell manipulation and mechanical

characterization [3]–[10]. For instance, Gultepe et al. demon-

strated the feasibility of an in vivo biopsy of the porcine

bile duct using thermally-responsive grippers [11]. Ichikawa

et al. demonstrated the enucleation of bovine oocytes using

untethered millimeter-scale grippers [9].

In the aforementioned studies, the small size of the

grippers has been exploited to perform tasks that would

otherwise be unfeasible with traditional techniques. Nonethe-

less, at least four main challenges need to be overcome

before grippers can be broadly used in biomedical applica-

tions; (1) Further miniaturization of the grippers combined

F. Ongaro, F. van den Brink, M. Abayazid and S. Misra are affiliated withthe Surgical Robotics Laboratory, Department of Biomechanical Engineer-ing, MIRA-Institute for Biomedical Technology and Technical Medicine,University of Twente, The Netherlands. S. Misra is also affiliated withthe Department of Biomedical Engineering, University of Groningen andUniversity Medical Centre Groningen, The Netherlands.

C. Yoon and D.H. Gracias are affiliated with the Department of Mate-rials Science and Engineering, Johns Hopkins University, Baltimore, USA.S.H. Oh and D.H. Gracias are affiliated with the Department of Chemicaland Biomolecular Engineering, Johns Hopkins University, Baltimore, USA.

t=0s t=30s t=60s t=95s

23◦C 24.5◦C 25◦C 30◦C

xy

Fig. 1. Top: Photographs of the electromagnetic and thermal systemsused to control the soft grippers. The system consists of 6 orthogonally-configured coils, and a Peltier element. The electromagnetic coils have acutoff frequency of 70 Hz and a maximum current rating of 1 A. Thesystem generates a maximum magnetic field and magnetic field gradient of15 mT and 60 mT/m, respectively. Bottom: Snapshots showing the grippergrasping a micro-sized bead. The scale bar is 0.8 mm.

with untethered operation has to be achieved. (2) Precise

closed-loop control of motion and grasping of the grip-

pers has to be realized. (3) The grippers have to reliably

manipulate micro-sized objects. (4) The grippers have to

be fabricated using biocompatible materials and operate

in a manner that poses no risk to humans.

Size reduction and untethered actuation are critical to

enable maneuverability of small-scale grippers in hard-to-

reach environments. Conventional robotic approaches with

electrical motors and actuators do not allow for significant

miniaturization of the electronic components and on-board

batteries. Hence, the use of wirelessly powered self-folding

robots have drawn interest and shown promising results

[12]–[18]. A family of prominent self-folding structures are

composed of hydrogels. Hydrogels have several attractive

properties of relevance to untethered small robots. Many can

be constructed with biocompatible and even biodegradable

polymer chains or cross-linkers making them attractive for

biomedical applications. They can function in aqueous me-

dia of relevance to biology and medicine. Their soft and

squishy nature allows them to mimic the touch and feel of

biological and even human appendages. Finally, they can be

photopatterned into definite shapes so that they can change

their configuration on swelling and shrinkage [19].

A. Related Work

In this paper, self-folding is achieved by constraining the

swelling of the hydrogel using a stiff polymer (SU-8). As

previously demonstrated this combination of a stiff polymer

with a reversibly swelling hydrogel can be used to create

microtools with significant strength and applicability for

grasping applications. In a related study, Breger et al. doped

the polymer with magnetic nanoparticles to demonstrate

open-loop control of soft grippers [20]. We utilize similarly

designed grippers to realize closed-loop control and obtain

levels of precision and reliability that are not achievable in

open-loop. Closed-loop control of hydrogel grippers have

also been reported by Fusco et al. [14], [15]. The main

differences between [14], [15] and our study are: a) The

previously reported grippers in [14], [15] were not magnetic

themselves and so magnetic motion control was only possible

when they gripped onto a magnetic object. (b) Previously

near-IR radiation was used to heat the grippers whereas

here we use a Peltier element, and (c) the numerical results

and analysis of the closed-loop motion control and pick-

and-place tasks were not reported so the accuracy and of

previously reported tasks remains unclear.

B. Contribution

In this study, we demonstrate and analyze the perfor-

mance of loaded and unloaded grippers that can be pre-

cisely localized and positioned in two-dimensional space

using closed-loop motion control. We exploit the self-

folding properties of the hydrogel to endow temperature

control and regulate the configuration of the grippers.

Finally, through the synergy of magnetic and tempera-

ture control, we demonstrate the capability of grippers to

execute pick-and-place of micro-sized objects.

The paper is organized as follows: Section II presents

the electromagnetic system, fabrication process and char-

acterization of the soft grippers. Section III describes the

used tracking and control techniques. Section IV presents

and discusses the experimental results. Finally, Section V

concludes and provides directions for future work.

II. EXPERIMENTAL SETUP

In this section, the magnetic and thermal systems are

described. Subsequently, we illustrate the fabrication pro-

cess of the gripper and the techniques applied for their

magnetic and thermal characterization.

A. Magnetic and Thermal Systems

Our magnetic system consists of six orthogonally oriented

electromagnets surrounding a Petri dish with an attached

Peltier element (Fig. 1) [21]. The electromagnets are con-

trolled using a proportional-integral-derivative (PID) con-

troller [22]. Each electromagnet is powered by an Elmo

Whistle 1/60 servo controller (Elmo Motion Control, Petach-

Tikva, Israel). A color camera (Point Grey Research Inc.,

24◦ C

25.5◦ C

25◦ C

26.5◦ C

Fig. 2. A schematic of the fabrication process of the soft grippers: (a) SU-8is spin-coated on a polyvinyl alcohol (PVA) sacrificial layer. (b) The SU-8film is photopatterned and exposed to ultraviolet (UV) light. (c) A 95% poly-N-isopropylacrylamide (pNIPAM-AAc) and 5% biocompatible Fe2O3 layeris deposited on the SU-8 layer. (d) The coated surface is photopatternedand exposed to UV light to obtain segmented, multi-fingered, bilayergrippers with rigid phalanges and flexible joints. (e) Schematic images ofthe untethered grippers in open and closed (grasping) configurations. Alsoshown is a side-view of a single hinge.

Richmond, Canada) and a microscope (Mitutoyo, Kawasaki,

Japan) are used to track the grippers.

A Peltier element is used to regulate the temperature of

the water where the soft grippers are floating. The element is

attached below the Petri dish with conductive double-sided

tape and controls its temperature by conduction. An Arduino

Uno (Arduino, Ivrea, Italy) micro-controller powers and

controls the Peltier element using Proportional-Derivative

(PD) control [22]. The PD temperature controller is able

to achieve a steady-state error of about 1◦ C and can heat

the water at an average rate of 10◦ C/min. A commercial

thermometric probe is used in the PD control loop.

B. Fabrication of Grippers

In order to fabricate the segmented SU-8/continuous poly-

N-isopropylacrylamide (pNIPAM-AAc) bilayer grippers, a

90% hydrolyzed polyvinyl alcohol (PVA) sacrificial layer is

spin coated onto a silicon (Si) wafer and then baked at 115◦

C for 5 minutes (Fig. 2). SU-8 is then spin coated on the

PVA at 2000 rpm followed by a pre-bake process at 70◦

C for 1 minute, 115◦ C for 3 minutes, and 70◦ C for 1

minute. The 21µm-thick SU-8 film is then photopatterned

using a photomask and exposed to 180 mJ/cm2 ultraviolet

(UV) light (365 nm) to initiate crosslinking. Further, post-

baking is carried out at 70◦ C for 1 minutes, 115◦ C for 3

minutes, and 70◦ C for 1 minute. Uncrosslinked portions of

the SU-8 are removed using a commercial SU-8 developer

for 1 minute and then washed with acetone for 1 second

and isopropyl alcohol (IPA) for 10 seconds before being

dried with compressed air. In order to make the 34µm-

thick magnetic second layer of pNIPAM-AAc, 5% w/w

biocompatible iron (III) oxide (Fe2O3, Sigma-Aldrich, St.

Louis, USA) 50 nm nanoparticles are incorporated into the

pNIPAM-AAc stock solution [20]. The obtained pNIPAM-

AAc solution including Fe2O3 is patterned on the previ-

ously photopatterned SU-8 segments using a second dark

8500

5500

6000

8000 9000

Two-tip dipole10

86

422

46

8

40

80

70

60

50

10

N

S

x [mm]y [mm]

tim

e[s

]

x [µm]

y[µ

m] D=452 µm

Fig. 3. Schematic of the trajectory of the two-tip dipole during theU-turn experiments for magnetic characterization. Left inset: A graphicalrepresentation of the magnetic dipole moment of the soft gripper as asuperposition of the magnetic dipole moments of its two-tip dipoles.

field mask and aligned in non-contact mode using spacers.

Once deposited and aligned, pNIPAM-AAc is exposed to

40 mJ/cm2 UV light to initiate crosslinking. A wash in

acetone and IPA is used to remove uncrosslinked pNIPAM-

AAc before drying using compressed air. Finally, the wafer

is immersed in DI water overnight to completely dissolve the

PVA sacrificial layer. When fully opened, the grippers have

an hexagram shape with a tip-to-tip dimension of 4 mm.

When fully closed, the grippers have the shape of a sphere

with an approximately 0.4 mm radius.

C. Magnetic Characterization of Grippers

We characterize the grippers resulting from this fabrication

process evaluating their magnetic dipole moment and thermal

behavior (Sec. II-D). The magnetic dipole moment of the

grippers (mg ∈ R3×1) is required for modeling purposes

(Sec. III-A). In order to evaluate mg, the grippers are

assumed to have a uniform Fe2O3 distribution. We divide

the six-tip gripper in three pairs of counterposed two-tip

dipoles. The magnetic dipole moments of the latter ones

(mtips ∈ R3×1) can be superposed to obtain mg (Fig.

3). The magnitude of mtips is experimentally measured

using the U-turn technique, after after removing four

tips from the gripper to obtain two-tips dipole[23]. The

two-tip dipole align along the magnetic field lines, reversing

the field direction cause them to perform a U-turn whose

diameter (D) is given by

D =απ|P|

|mtips||B(P)|, (1)

where P ∈ R3×1 is linear velocity of the dipole, and α is

its rotational drag coefficient. We calculate the value of α to

be 2.2×10−11 Am2sT approximating the two-tip dipole by

a cylinder [24]. In order to determine the magnetic dipole

moment, we apply uniform magnetic fields of 3.5 mT. The

fields are reversed to initiate the U-turn. The experiment is

repeated 20 times. The average U-turn diameter and velocity

are 0.19±0.05 mm and 0.73±0.13 mm/s, respectively. Using

(1) we obtain |mtips| =3.5×10−8 Am2. The direction of

24 24.5 25 25.5 26 26.5 270

0.2

0.4

0.6

0.8

1

Clo

sing

Open

ing

C

Temperature [◦C]

Fig. 4. Results of the opening and closing characterization of thesoft grippers (15 experimental trials): The red and blue lines show theaverage configuration of the grippers when they are heated and cooled,respectively. The corresponding shaded areas depict the standard deviations.The coefficient C is an indicator of the configuration of the grippers andvaries from 1 (for an open configuration) to 0 (for a closed configuration).

The value is computed as C =D(T )−Dclosed

Dopen−Dclosed, where D(T ) is the

diameter of the contour of the gripper at temperature T , Dclosed andDopen are the diameter values for the completely closed and open gripper,respectively. The scale bar is 0.8 mm.

mtips is determined using mtips = pd = |mtips|d

|ℓ| where

p ∈ R is the magnetic pole strength and d ∈ R3×1

is the vector separating the two poles [25]. Finally, the

magnetic dipole moment of the gripper is computed as the

superposition of three rotated two-tip dipoles. The mag-

nitude of mg results 7×10−8 Am2 while its orientation

with respect to the gripper is represented in Fig. 3. We

note that the adopted technique overestimates the magnetic

dipole moment of the central overlapping part. However, this

section is assumed to have a negligible effect on the overall

magnetic dipole moment due to its small d.

D. Thermal Characterization

We also characterize the thermal response of the grip-

pers. For this purpose, the temperature of the water was

increased until the gripper was fully closed, and then de-

creased to room temperature. During this procedure, the

gripper changes its configuration from star-shaped to spher-

ical, and back (Fig. 4). Therefore, we use the diameter of

the gripper to evaluate its configuration (Sec. III-B). Five

successive opening and closing cycles were analyzed for

three different grippers. The results are shown in Fig. 4.

The grippers on average completely opened at temperatures

below 24◦ C and fully closed above 27◦ C. However, we

noticed a variance of these boundaries depending on the

temperature dynamics. Open grippers closed at lower tem-

peratures than the ones at which closed grippers opened. This

advantageous behavior makes the grippers more responsive

to thermal control actions.

III. TRACKING AND CONTROL

This section presents the modeling and control of our

setup. Also the tracking procedure for position extraction

and prediction is commented upon.

(a) (b) (c) (d)

Fig. 5. Flowchart illustrating the steps in the contour-extraction process for the soft grippers. (a) Input image from the microscope in Red-Green-Blue(RGB) colorspace. (b) The input is converted to Hue-Saturation-Value (HSV) color representation to separate chrominance from luminance and achieveglare robustness. (c) The image binarized using a Gaussian-window threshold after the application of a median filter. (d) The extracted contour of thegripper. The scale bar is 0.8 mm.

A. Modeling and Control

Magnetic-based wireless control techniques are used for

the motion control of grippers. These are based on the

ability to map the currents at the electromagnets into the

electromagnetic forces exerted on the grippers using,

F(P) = (mmg · ∇)B(P) = Λ(mmg,P)I , (2)

where F are the electromagnetic forces acting on the soft

gripper, B(P) ∈ R3×1 and I ∈ R

6×1 are the magnetic

field produced by the electromagnets and their currents, re-

spectively, and Λ(mmg,P) ∈ R3×6 is the actuation matrix,

which maps the input currents into magnetic forces [26].

The forces are then regulated using a two-input, three-output

Multi-Input Multi-Output (MIMO) PID controller. The two

inputs of the regulator are the x− and y−coordinates of the

gripper. The output F is subsequently mapped into I using

the pseudo-inverse of Λ(mmg,P) [27].

The computation of the force-current map (Λ) requires

the knowledge of B(P) and mmg. The B(P) of our setup

has been evaluated in previous studies, using a finite el-

ements model analysis, and successively verified using a

calibrated three-axis Hall magnetometer [28]. The value of

mmg is estimated in Sec. II-C, the tracking procedure to

obtain P is presented in Sec. III-B.

B. Tracking

The tracking process is composed of two steps. The first

step aims at extracting the gripper contour from the input

image, and is presented in Fig. 5. The points of this contour

are subsequently mapped to the imaginary plane at the

beginning of the successive step. The selected equation for

this mapping is zn = xn + iyn for n = 0, 1, ..., N where N

is the number of the re-sampled contour points, xn and ynare the coordinates of the n-th re-sampled point, and i is

the imaginary number [29]. We use this uniform sampled

complex representation to calculate the Discrete Fourier

Transform (DFT) coefficients by,

Zk =1

N

N−1∑

n=1

zn exp

(

−i2πnk

N

)

for n = 0, 1, ..., N − 1,

(3)

where k ∈ Z goes from -15 to 16. The DFT coefficients

provide us the position, scale and orientation of the gripper

[29]. In order to increase noise rejection, we ignore all the

contours that are not 6-fold symmetric by only tracking

objects that satisfy the following conditions [30]:

Z−5 >2

N − 2

(

16∑

k=−15

Zk − Z1

)

, (4)

Z7 >2

N − 2

(

16∑

k=−15

Zk − Z1

)

, (5)

where Zk are normalized Fourier descriptors. Furthermore,

we set a threshold constraint on the ratio between con-

tour and area of the contour. This value must be be-

tween 0.5 and 1 in order to avoid erroneous tracking of

other 6-fold symmetric objects.

For the purpose of dealing with uncertainties in the

tracking, we implemented a standard Kalman filter [31].

The Kalman filter provides a one-step ahead estimation of

positions and velocities, using current positions and control-

input. The process noise is assumed to be a random variable

with a Gaussian distribution N(0, Q), Q ∈ R4×4 being an

empirically determined covariance matrix.

IV. RESULTS

In this section, we evaluate the performance and capa-

bilities of the grippers. First motion control experiments

are performed. Following these experiments, through the

cooperation of motion and temperature closed-loop control,

we assess the performance and capabilities of the grippers

in pick-and-place tasks.

A. Motion Control of Grippers

In these experiments, we evaluate closed-loop control soft

grippers during point-to-point control and tracking of circular

and square paths (Fig. 6). The experiments are performed

both when the grippers are unloaded, and loaded with a

500 µm diameter polystyrene bead (micro-sized payload).

The circular path has a radius of 3 mm. The square path has

sides of 6 mm. In order to verify the statistical reliability

of the results, we perform 50 experimental trials for each

task, using 10 different grippers without the micro-sized

payload. The experimental results are tabulated in Table I.

The grippers without micro-sized payload move with an

0

10

30

20

40

50

8

4

2

6 8

4

6

24

23

5556

22

x [mm]y [mm]

tim

e[s

]

x [µm]

y[µ

m]

×102

×102

(a)

10

9

8

7

6

5

4

3

21098765432

-5087654

x/y [mm]

0

100

50

x [mm]

y[m

m]

erro

r[µ

m]

(b)

2

3

4

5

6

7

8

9

10

2 3 4 5 6 7 8 9 10

300

2 4 6 8

100

200

0

x [mm]

y[m

m]

y [mm]

erro

r[µ

m]

(c)

Fig. 6. Representative closed-loop motion control experimental results of a gripper. (a) An example of point-to-point motion control experiments. Thered lines represents the setpoint, the blue line the trajectory of the gripper, and the red circles the Region of Convergence (ROC). (b) and (c) depict thetrajectory following experiments. The green dashed path represents the reference trajectory, the black line shows the path of the gripper, and the red arearepresents the standard deviation for the corresponding point among all the experiments. The insets show the positioning error in the highlighted parts ofthe trajectories. Please refer to the accompanying video for the experiments.

average velocity and positioning error of 0.72±0.13 mm/s

and 0.11±0.1 mm, respectively. Please refer to the accom-

panying video for the experiments.

The average positioning error for the 150 experimental

trials is 3% of the body length of the gripper. The error never

reaches values above 5.5% of the gripper body length and

such errors only occur during sharp turns, when the magnetic

dipole moment of the gripper and the magnetic field are the

least aligned, resulting in a weaker magnetic force (2).

In order to determine whether the performance difference

among different grippers can be considered statistically neg-

ligible, we performed a Two One-Sided T-test (TOST) [32].

The tests revealed statistical equivalence, with 90% interval

confidence, suggesting that all soft grippers behave similarly.

Consequently, the number of experimental trials of motion

control experiments of grippers with the micro-sized pay-

load was reduced to 15 trials. These experiments followed

the previously presented methodology and the results are

tabulated in Table I. The grippers with the micro-sized

payload moved 52% faster than grippers without the micro-

sized payload, with an average velocity and positioning error

of 1.09±0.07 mm/s and 0.17±0.23 mm, respectively. We

attribute this increase in speed to the compact folded ball-

shape of the gripper which reduces the shear forces with

the water and the side-walls of the dish.

B. Pick-and-Place Tasks

In this section, we highlight the ability of grippers to

perform pick-and-place tasks. A gripper is positioned above

a 500 µm spherical bead. Once the position is reached,

the temperature is raised to 40◦ C. This causes the grip-

per to close, and grasp the bead. Therefore, the micro-

sized payload is captured within the gripper and can be

dragged to the desired dropping location. The releasing

procedure is activated by decreasing the temperature below

25◦ C. The experiment is repeated five times with an

average positioning error of the bead of 0.57±0.33 mm.

The micro-sized payload is transported for 1.5 cm with an

average velocity of 1.09±0.07 mm/s. Please refer to the

accompanying video for the experiments.

V. CONCLUSIONS AND FUTURE WORK

In this paper, we characterize soft self-folding

grippers and analyze their capabilities and performance.

Moreover, we demonstrate their ability to pick-and-

place micro-scale objects. The gripper can be localized

and follow trajectories with average positioning

errors of 0.03 body lengths and speeds of 0.2

body lengths per second. Pick-and-place tasks are

completed at average velocity of 1.09±0.07 mm/s and

positioning error of the micro-sized object of 0.57 mm.

The experiments are enabled via two significant advances

in materials science and robotics which include, (1) The

fabrication of reversible soft-actuating grippers that harness

mechanical energy and shape change from swelling; hence

they do not need wires, batteries or external power sources

for actuation. (2) The ability to control the local temperature

and magnetic field in a closed-loop with high accuracy.

TABLE I

EXPERIMENTAL MOTION CONTROL RESULTS OF SOFT GRIPPERS FOR POINT-TO-POINT, CIRCULAR AND SQUARE TRAJECTORIES. THE AVERAGE

SPEEDS AND EUCLIDEAN-NORM OF AVERAGE POSITIONING ERROR ARE REPORTED WITH THE RESPECTIVE STANDARD DEVIATION (150 AND 15

EXPERIMENTAL TRIALS ARE CONDUCTED FOR GRIPPERS WITHOUT AND WITH THE MICRO-SIZED PAYLOAD, RESPECTIVELY).

Grippers without micro-sized payload Grippers with micro-sized payloadExperiment Average speed Error Average speed Error

Point to point 0.8±0.1 mm/s 0.12±0.05 mm 1.1±0.06 mm/s 0.23±0.04 mmCircular 0.62±0.13 mm/s 0.12±0.09 mm 1.08 ±0.04 mm/s 0.17±0.12 mmSquare 0.73±0.11 mm/s 0.09±0.1 mm 1.08±0.04 mm/s 0.13±0.12 mm

As part of future work, grippers will be controlled in three-

dimensional space. Furthermore, fully-autonomous pick-and-

place of irregularly shaped objects will be studied. Moreover,

advanced control techniques (e.g., cascade control) will be

used to optimize the tracking of more intricate paths. Also,

the Fe2O3 pattern of the grippers will be exploited in order to

utilize the presented system in clinically-relevant applications

using medical imaging systems.

ACKNOWLEDGMENT

This research has received funding from the European Re-

search Council (ERC) under the European Union’s Horizon

2020 Research and Innovation programme (Grant Agreement

#638428 - project ROBOTAR: Robot-Assisted Flexible Nee-

dle Steering for Targeted Delivery of Magnetic Agents).

The research reported in this publication was also sup-

ported by the National Institute of Biomedical Imaging and

Bioengineering of the National Institutes of Health (NIH)

under Award Number R01EB017742. The content is solely

the responsibility of the authors and does not necessarily

represent the official views of the NIH.

REFERENCES

[1] S. Martel and M. Mohammad, “Using a swarm of self-propellednatural microrobots in the form of flagellated bacteria to perform com-plex micro-assembly tasks,” in Proceedings of the IEEE International

Conference on Robotics and Automation (ICRA), pp. 500–505, Alaska,USA, May 2010.

[2] M. Sitti, H. Ceylan, W. Hu, J. Giltinan, M. Turan, S. Yim, and E. Diller,“Biomedical applications of untethered mobile milli/microrobots,”Proceedings of the IEEE, vol. 103, no. 2, pp. 205–224, 2015.

[3] N. Dechev, W. Cleghorn, and J. K. Mills, “Microassembly of 3-dmicrostructures using a compliant, passive microgripper,” Journal of

Microelectromechanical Systems, vol. 13, no. 2, pp. 176–189, 2004.

[4] J. S. Randhawa, T. G. Leong, N. Bassik, B. R. Benson, M. T.Jochmans, and D. H. Gracias, “Pick-and-place using chemically actu-ated microgrippers,” Journal of the American Chemical Society, vol.130, no. 51, pp. 17 238–17 239, 2008.

[5] M. M. S. Mousavi, G. D. Pasquale, A. Som, and E. Brusa, “A novelSU-8 microgripper with external actuator for biological cells manipu-lation,” in Proceedings of Symposium on Design, Test, Integration &

Packaging of MEMS and MOEMS (DTIP), Aix-en-Provence, France,May 2011.

[6] T. Yoneyama, T. Watanabe, H. Kagawa, J. Hamada, Y. Hayashi, andM. Nakada, “Force detecting gripper and flexible micro manipulatorfor neurosurgery,” in Proceedings of the IEEE Engineering in Medicine

and Biology Society (EMBS), pp. 6695–6699, Boston, MA, USA,August 2011.

[7] S. Tottori, L. Zhang, F. Qiu, K. K. Krawczyk, A. Franco-Obregon, andB. J. Nelson, “Magnetic helical micromachines: fabrication, controlledswimming, and cargo transport,” Advanced materials, vol. 24, no. 6,pp. 811–816, 2012.

[8] E. Diller and M. Sitti, “Three-dimensional programmable assemblyby untethered magnetic robotic micro-grippers,” Advanced Functional

Materials, vol. 24, no. 28, pp. 4397–4404, 2014.

[9] A. Ichikawa, S. Sakuma, F. Arai., and S. Akagi, “Untethered micro-robot with gripping mechanism for on-chip cell surgery utilizing outermagnetic force,” in Proceedings of the IEEE International Conference

on Robotics and Automation (ICRA), pp. 3795–3800, Hong Kong,China, May 2014.

[10] K. Malachowski, M. Jamal, Q. Jin, B. Polat, C. J. Morris, and D. H.Gracias, “Self-folding single cell grippers,” Nano Letters, vol. 14,no. 7, pp. 4164–4170, 2014.

[11] E. Gultepe, J. S. Randhawa, S. Kadam, S. Yamanaka, F. M. Selaru,E. J. Shin, A. N. Kalloo, and D. H. Gracias, “Biopsy with thermally-responsive untethered microtools,” Advanced Materials, vol. 25, no. 4,pp. 514–519, 2012.

[12] J. S. Randhawa, K. E. Laflin, N. Seelam, and D. H. Gracias,“Microchemomechanical systems,” Advanced Functional Materials,vol. 21, no. 13, pp. 2395–2410, 2011.

[13] K. Malachowski, J. Breger, H. R. Kwag, M. O. Wang, J. P. Fisher,F. M. Selaru, and D. H. Gracias, “Stimuli-responsive theragrippers forchemomechanical controlled release,” Angewandte Chemie, vol. 126,no. 31, pp. 8183–8187, 2014.

[14] S. Fusco, M. S. Sakar, S. Kennedy, C. Peters, R. Bottani, F. Starsich,A. Mao, G. A. Sotiriou, S. Pane, S. E. Pratsinis et al., “An integratedmicrorobotic platform for on-demand, targeted therapeutic interven-tions,” Advanced Materials, vol. 26, no. 6, pp. 952–957, 2014.

[15] S. Fusco, M. S. Sakar, S. Kennedy, C. Peters, S. Pane, D. Mooney, andB. J. Nelson, “Self-folding mobile microrobots for biomedical applica-tions,” in Robotics and Automation (ICRA), 2014 IEEE International

Conference on, pp. 3777–3782. IEEE, 2014.[16] J. C. Kuo, H. W. Huang, S. W. Tung, and Y. J. Yang, “A hydrogel-

based intravascular microgripper manipulated using magnetic fields,”Sensors and Actuators A: Physical, vol. 211, pp. 121–130, 2014.

[17] S. Miyashita, S. Guitron, M. Ludersdorfer, C. R. Sung, and D. Rus,“Untethered miniature origami robot that self-folds, walks, swims, anddegrades,” in Proceedings of the IEEE International Conference on

Robotics and Automation (ICRA), pp. 1490–1496, Seattle, WA, USA,May 2015.

[18] H. Li, G. Go, S. Y. Ko, J.-O. Park, and S. Park, “Magnetic actuated ph-responsive hydrogel-based soft micro-robot for targeted drug delivery,”Smart Materials and Structures, vol. 25, no. 2, p. 027001, 2016.

[19] D. H. Gracias, “Stimuli responsive self-folding using thin polymerfilms,” Current Opinion in Chemical Engineering, vol. 2, no. 1, pp.112–119, 2013.

[20] J. C. Breger, C. Yoon, R. Xiao, H. R. Kwag, M. O. Wang, J. P. Fisher,T. D. Nguyen, and D. H. Gracias, “Self-folding thermo-magneticallyresponsive soft microgrippers,” ACS Applied Materials & Interfaces,vol. 7, no. 5, pp. 3398–3405, 2015.

[21] A. Sanchez, Y. M. Sadek, I. S. M. Khalil, and S. Misra, “Mobi-mag: A compact device for medical research using wireless controlof magnetic microrobots,” in Proceedings of the Design of Medical

Devices Conference-Europe, pp. 100–101, Delft, Netherlands, October2014.

[22] G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback control

of dynamics systems, 1994.[23] A. S. Bahaj, P. A. B. James, and F. D. Moeschler, “An alternative

method for the estimation of the magnetic moment of non-sphericalmagnetotactic bacteria,” IEEE Transactions on Magnetics, vol. 32,no. 5, pp. 5133–5135, 1996.

[24] Y. R. Chemla, H. L. Grossman, T. S. Lee, J. Clarke, M. Adamkiewicz,and B. B. Buchanan, “A new study of bacterial motion: supercon-ducting quantum interference device microscopy of magnetotacticbacteria,” Biophysical journal, vol. 76, no. 6, pp. 3323–3330, 1999.

[25] W. F. Brown, “Magnetostatic principles,” in Ferromagnetism. North-Holland Amsterdam, 1962.

[26] I. S. M. Khalil and S. Misra, “Control characteristics of magneto-tactic bacteria: Magnetospirillum Magnetotacticum strain MS-1 andMagnetospirillum Magneticum strain AMB-1,” IEEE Transactions on

Magnetics, vol. 50, no. 4, pp. 1–11, 2014.[27] I. S. M. Khalil, L. Abelmann, and S. Misra, “Magnetic-based motion

control of paramagnetic microparticles with disturbance compensa-tion,” IEEE Transactions on Magnetics, vol. 50, no. 10, pp. 1–10,2014.

[28] A. Sanchez, V. Magdanz, O. G. Schmidt, and S. Misra, “Magneticcontrol of self-propelled microjets under ultrasound image guidance,”in Proceedings of the IEEE RAS & EMBS International Conference on

Biomedical Robotics and Biomechatronics, pp. 169–174, Sao Paulo,Brazil, August 2014.

[29] F. Van der Heijden, Image based measurement systems: object recog-

nition and parameter estimation. John Wiley & Sons Ltd, 1994.[30] M. He, “The faber polynomials for m-fold symmetric domains,”

Journal of Computational and Applied Mathematics, vol. 54, no. 3,pp. 313–324, 1994.

[31] P. R. Belanger, P. Dobrovolny, A. Helmy, and X. Zhang, “Estimation ofangular velocity and acceleration from shaft-encoder measurements,”The International Journal of Robotics Research, vol. 17, no. 11, pp.1225–1233, 1998.

[32] G. B. Limentani, M. C. Ringo, F. Ye, M. L. Bergquist, and E. O. Mc-Sorley, “Beyond the t-test: statistical equivalence testing,” Analytical

Chemistry, vol. 77, no. 11, pp. 221–226, 2005.